메뉴 건너뛰기




Volumn 134, Issue 1, 2005, Pages 116-139

Kernel estimates of the mean and the volatility functions in a nonlinear autoregressive model with ARCH errors

Author keywords

Ergodic processes; Kernel estimate; Martingale difference; Mixing processes; Normality; Prediction; Variance function

Indexed keywords


EID: 20044393354     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jspi.2004.01.019     Document Type: Article
Times cited : (16)

References (36)
  • 1
    • 0000115649 scopus 로고
    • Non-strong mixing autoregressive processes
    • D.W.K. Andrews Non-strong mixing autoregressive processes J. Appl. Probab. 21 1984 930-934
    • (1984) J. Appl. Probab. , vol.21 , pp. 930-934
    • Andrews, D.W.K.1
  • 2
    • 0001052198 scopus 로고
    • Ergodicity of nonlinear first order autoregressive models
    • R.N. Bhattacharya C. Lee Ergodicity of nonlinear first order autoregressive models J. Theoret. Probab. 8 1995 207-219
    • (1995) J. Theoret. Probab. , vol.8 , pp. 207-219
    • Bhattacharya, R.N.1    Lee, C.2
  • 4
    • 0012009381 scopus 로고
    • Strong mixing of linear stochastic processes
    • K.C. Chanda Strong mixing of linear stochastic processes J. Appl. Probab. 11 1974 401-408
    • (1974) J. Appl. Probab. , vol.11 , pp. 401-408
    • Chanda, K.C.1
  • 5
    • 0000032630 scopus 로고
    • A limit theorem for the maximum of autoregressive processes with uniform marginal distributions
    • M.R. Chernick A limit theorem for the maximum of autoregressive processes with uniform marginal distributions Ann. Probab. 9 1981 145-149
    • (1981) Ann. Probab. , vol.9 , pp. 145-149
    • Chernick, M.R.1
  • 6
    • 0033262354 scopus 로고    scopus 로고
    • Geometric ergodicity of nonlinear time series
    • D.B.H. Cline H.H. Pu Geometric ergodicity of nonlinear time series Statist. Sinica 4 1999 1103-1118
    • (1999) Statist. Sinica , vol.4 , pp. 1103-1118
    • Cline, D.B.H.1    Pu, H.H.2
  • 7
    • 84972804609 scopus 로고
    • Nonparametric regression
    • G. Collomb Nonparametric regression an up to date bibliography Statistics 2 1985 309-324
    • (1985) Statistics , vol.2 , pp. 309-324
    • Collomb, G.1
  • 8
    • 0001908707 scopus 로고
    • Strong convergence rates in robust non parametric time series analysis and prediction: Kernel regression estimation for dependent observations
    • G. Collomb W. Härdle Strong convergence rates in robust non parametric time series analysis and prediction: Kernel regression estimation for dependent observations Stochastic Process. Appl. 23 1 1986 77-89
    • (1986) Stochastic Process. Appl. , vol.23 , Issue.1 , pp. 77-89
    • Collomb, G.1    Härdle, W.2
  • 9
    • 0001580091 scopus 로고    scopus 로고
    • Nonparametric estimation of a regression function and its derivatives under an ergodic hypothesis
    • M. Delecroix A.C. Rosa Nonparametric estimation of a regression function and its derivatives under an ergodic hypothesis J. Nonparametric Statist. 6 1996 367-382
    • (1996) J. Nonparametric Statist. , vol.6 , pp. 367-382
    • Delecroix, M.1    Rosa, A.C.2
  • 10
    • 0012276078 scopus 로고
    • Testing the function defining a nonlinear autoregressive time series
    • J. Diebolt Testing the function defining a nonlinear autoregressive time series Stochastic Process. Appl. 36 1990 85-106
    • (1990) Stochastic Process. Appl. , vol.36 , pp. 85-106
    • Diebolt, J.1
  • 11
    • 38249009969 scopus 로고
    • Multivariate regression estimation with errors-in-variables: Asymptotic normality for mixing processes
    • J. Fan E. Masry Multivariate regression estimation with errors-in-variables: Asymptotic normality for mixing processes J. Multivariate anal. 43 1992 237-271
    • (1992) J. Multivariate Anal. , vol.43 , pp. 237-271
    • Fan, J.1    Masry, E.2
  • 12
    • 0000871211 scopus 로고    scopus 로고
    • Efficient estimation of conditional variance functions in stochastic regression
    • J. Fan Q. Yao Efficient estimation of conditional variance functions in stochastic regression Biometrika 85 1998 645-660
    • (1998) Biometrika , vol.85 , pp. 645-660
    • Fan, J.1    Yao, Q.2
  • 13
    • 0003012835 scopus 로고
    • Probabilistic properties of the β-ARCH model
    • D. Guégan J. Diebolt Probabilistic properties of the β -ARCH model Statist. Sinica 4 1994 71-87
    • (1994) Statist. Sinica , vol.4 , pp. 71-87
    • Guégan, D.1    Diebolt, J.2
  • 14
    • 18044402349 scopus 로고    scopus 로고
    • Non-mixing properties of long memory processes
    • D. Guégan S. Ladoucette Non-mixing properties of long memory processes C.R. Acad. Sci. Paris 333 2001 373-376
    • (2001) C.R. Acad. Sci. Paris , vol.333 , pp. 373-376
    • Guégan, D.1    Ladoucette, S.2
  • 17
    • 0000961658 scopus 로고    scopus 로고
    • Local polynomial estimation of the volatility function in nonparametric autoregression
    • W. Härdle A. Tsybakov Local polynomial estimation of the volatility function in nonparametric autoregression Econometrica 81 1997 223-242
    • (1997) Econometrica , vol.81 , pp. 223-242
    • Härdle, W.1    Tsybakov, A.2
  • 19
    • 0000272104 scopus 로고
    • Data-driven bandwidth choice for density estimation based on dependent data
    • J.D. Hart P. Vieu Data-driven bandwidth choice for density estimation based on dependent data Ann. Statist. 18 1990 873-890
    • (1990) Ann. Statist. , vol.18 , pp. 873-890
    • Hart, J.D.1    Vieu, P.2
  • 21
    • 0040153567 scopus 로고    scopus 로고
    • Exponential-type inequalities for martingale difference sequences
    • N. Laïb Exponential-type inequalities for martingale difference sequences application to non-parametric regression estimation Commun. Statist. Theory and Methods Ser. A 28 1999a 1565-1576
    • (1999) Commun. Statist. Theory and Methods Ser. A , vol.28 , pp. 1565-1576
    • Laïb, N.1
  • 22
    • 0040708924 scopus 로고    scopus 로고
    • Uniform consistency of the partitioning estimate under ergodic conditions
    • N. Laïb Uniform consistency of the partitioning estimate under ergodic conditions J. Austral. Math. Soc. Ser. A 67 1999b 1-14
    • (1999) J. Austral. Math. Soc. Ser. A , vol.67 , pp. 1-14
    • Laïb, N.1
  • 23
    • 0039550290 scopus 로고    scopus 로고
    • A robust nonparametric estimation of the autoregression function under an ergodic hypothesis
    • N. Laïb E. Ould-Saïd A robust nonparametric estimation of the autoregression function under an ergodic hypothesis Canad. J. Statist. 28 2000 817-828
    • (2000) Canad. J. Statist. , vol.28 , pp. 817-828
    • Laïb, N.1    Ould-Saïd, E.2
  • 24
    • 0032275771 scopus 로고    scopus 로고
    • On the geometric ergodicity of a non-linear autoregressive model with an autoregressive conditional heteroscedastic term
    • Z.D. Lu On the geometric ergodicity of a non-linear autoregressive model with an autoregressive conditional heteroscedastic term Statist. Sinica 8 1998 1205-1217
    • (1998) Statist. Sinica , vol.8 , pp. 1205-1217
    • Lu, Z.D.1
  • 25
    • 0033174127 scopus 로고    scopus 로고
    • Nonparametric regression with singular design
    • Z.Q. Lu Nonparametric regression with singular design J. Multivariate Anal. 70 1999 177-201
    • (1999) J. Multivariate Anal. , vol.70 , pp. 177-201
    • Lu, Z.Q.1
  • 26
    • 0031537053 scopus 로고    scopus 로고
    • Distribution-free strong consistency for nonparametric kernel regression involving nonlinear time series
    • Z.D. Lu P. Cheng Distribution-free strong consistency for nonparametric kernel regression involving nonlinear time series J. Statist. Plann. Inference 1 1997 67-86
    • (1997) J. Statist. Plann. Inference , vol.1 , pp. 67-86
    • Lu, Z.D.1    Cheng, P.2
  • 27
    • 0041364641 scopus 로고    scopus 로고
    • 1 geometric ergodicity of a multivariate nonlinear AR model with an ARCH term
    • 1 geometric ergodicity of a multivariate nonlinear AR model with an ARCH term Statist. Probab. Lett. 51 2001 121-130
    • (2001) Statist. Probab. Lett. , vol.51 , pp. 121-130
    • Lu, Z.D.1    Jiang, Z.2
  • 28
    • 0003009222 scopus 로고
    • Regression estimation with errors-in-variables for stationary processes
    • E. Masry Regression estimation with errors-in-variables for stationary processes J. Nonparametric Statist. 3 1993 13-36
    • (1993) J. Nonparametric Statist. , vol.3 , pp. 13-36
    • Masry, E.1
  • 29
    • 84974185463 scopus 로고
    • Nonparametric estimation and identification of nonlinear ARCH time series: Strong convergence and asymptotic normality
    • E. Masry D. Tjøstheim Nonparametric estimation and identification of nonlinear ARCH time series: Strong convergence and asymptotic normality Econom. Theory 11 1995 258-259
    • (1995) Econom. Theory , vol.11 , pp. 258-259
    • Masry, E.1    Tjøstheim, D.2
  • 30
    • 84986849734 scopus 로고
    • Nonparametric estimators for time series
    • P.M. Robinson Nonparametric estimators for time series J. Time Ser. Anal. 4 1983 185-208
    • (1983) J. Time Ser. Anal. , vol.4 , pp. 185-208
    • Robinson, P.M.1
  • 31
    • 0002591194 scopus 로고
    • Nonparametric regression estimation under mixing conditions
    • G.G. Roussas Nonparametric regression estimation under mixing conditions Stochastic Process. Appl. 36 1990 107-116
    • (1990) Stochastic Process. Appl. , vol.36 , pp. 107-116
    • Roussas, G.G.1
  • 32
    • 0000439527 scopus 로고
    • Optimal rate of convergence for nonparametric estimators
    • C.J. Stone Optimal rate of convergence for nonparametric estimators Ann. Statist. 8 1980 1348-1360
    • (1980) Ann. Statist. , vol.8 , pp. 1348-1360
    • Stone, C.J.1
  • 34
    • 0001917688 scopus 로고
    • Nonparametric function estimation involving time series
    • Y.M. Truong C.J. Stone Nonparametric function estimation involving time series Ann. Statist. 20 1992 77-97
    • (1992) Ann. Statist. , vol.20 , pp. 77-97
    • Truong, Y.M.1    Stone, C.J.2
  • 35
    • 0002645342 scopus 로고    scopus 로고
    • Strongly consistent nonparametric forecasting for stationary ergodic sequences
    • S. Yakowitz L. Györfi J. Kieffer Strongly consistent nonparametric forecasting for stationary ergodic sequences J. Multivariate Anal. 71 1999 24-41
    • (1999) J. Multivariate Anal. , vol.71 , pp. 24-41
    • Yakowitz, S.1    Györfi, L.2    Kieffer, J.3
  • 36
    • 0000278675 scopus 로고    scopus 로고
    • Nonparametric autoregression with multiplicative volatility and additive mean
    • L. Yang W. Härdle J.P. Nielsen Nonparametric autoregression with multiplicative volatility and additive mean J. Time Ser. Anal. 20 1999 579-604
    • (1999) J. Time Ser. Anal. , vol.20 , pp. 579-604
    • Yang, L.1    Härdle, W.2    Nielsen, J.P.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.